Ask Plex AI about problem 1
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Ask Plex AI about problem 1
Get hints, ask questions, and work through this problem step by step
Access custom-built, exam-style problems for -----------. Each problem has a full solution and mark-scheme, as well as AI grading and support.
Cartesian plane & lines
Access custom-built, exam-style problems for Cartesian plane & lines. Each problem has a full solution and mark-scheme, as well as AI grading and support.
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The line L passes through the points P(1,2) and Q(5,−2).
Find the slope of L.
Determine an equation for L in the form y=mx+c.
Find the midpoint of [PQ].
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The line L1 passes through the points A(1,−2) and B(1,3).
Write down the equation of L1.
A second line, L2, is perpendicular to L1 and passes through C(−4,5).
Find the equation of L2 in the form y=mx+c.
The point P lies on L1, and the point Q lies on L1 and L2.
Given that P is equidistant from A and Q, find the coordinates of P.
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The point U has coordinates (6,−3) and the point V has coordinates (−2,7). The point W has coordinates (1,−1).
Write down the coordinates of X, the midpoint of line segment UV.
Find the gradient of the line WX.
Find the equation of WX. Write your answer in the form
where a,b,d∈Z.
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In this question, distances are measured in meters.
A zip-line crossing a crocodile infested river can be modeled as a straight line between (0,28) and (50,20). The left and right banks of the river lie at (10,0) and (30,0), respectively.
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Calculate the length of the zip-line.
Determine the closest distance from the zip line to the river.
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Consider the points A(4,−1), B(−4,3) and C(−2,7). The line L passes through point C such that it is perpendicular to [AB].
Find the equation of L, and show that it passes through B.
Another point, D, is plotted such that the lines [AB] and [CD] bisect each other.
Find the coordinates of D.
Hence find the distance [AD].
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Consider the points A(−3,5) and B(5,−1) with midpoint M. The line L passes through M and is perpendicular to [AB].
Find the equation of L, giving your answer in the form y=mx+c.
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Flannery is a wizard brewing a batch of potions. She wants to brew some luck potions and some flight potions. Each contains the same rare specialized ingredients, dove feather dust and purple snake scales. A luck potion uses 3 pinches of dove feather dust and 2 purple snake scales. A flight potion uses 2 pinches of dove feather dust and 5 purple snake scales.
Flannery has 24 pinches of dove feather dust and 38 purple snake scales available. She wants to use all of the ingredients without leftovers.
Find the amount of each potion Flannery should make to use all of her supplies,
After Flannery gets her ingredients out of the cellar, her familiar, an orange cat named Ferguson, knocks over the jar of dove feather dust, spilling 4 pinches onto the floor and rendering them unusable. Flannery decides to brew fewer potions, but keep the same ratio of luck to flight potions. She cannot partially brew a potion.
Find the maximum number of each kind of potion that she can now brew.
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